Probabilty Distribution (Poisson Distribution)

In summary, the given conversation discusses the average number of days it rains in a town in October and the probability distribution of the number of days it rains, assuming independent events. The probability distribution is identified as a Poisson Distribution, with an expression of Pr(X=x) = [ (λ^x)*(e^-λ) ] / (x!), where λ is the expected number of days it will rain and x is the number of days it actually rains. The probability of it raining on any given day in October is calculated to be 0.332, and the probability distribution is stated as Pr(x) = [ (0.332^x)*(e^-0.332) ] / (x!). The writer also expresses some uncertainty about
  • #1
Daniel323
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Homework Statement


It rains on 10.3 days in the town in October on average. Let X denote the number of days in October on which it rains. Assume that rain falling on different days can be treated as independent events. (31 days in October).

Write down an expression for the probability that it rains on a given day in October, and hence state the probability distribution of X.

Homework Equations


I've identified the problem to be a Poission Distribution, with Pr(X=x) = [ (λ^x)*(e^-λ) ] / (x!)

The Attempt at a Solution


The probability of it raining on any given day in October = Expected no. of days it will rain / total no. of days = 10.3/31 = 0.332

Hence probability distribution of X would be Pr(x) = [ (0.332^x)*(e^-0.332) ] / (x!)

Sorry this is my first attempt at such a question and am not sure if I have done it right, or if I have even gone about it the right way.

If anyone knows how to tackle this problem, please let me know if I am right or wrong.

Thanks,
Daniel
 
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  • #2
Anyone have any ideas?
 

1. What is a Poisson distribution?

A Poisson distribution is a statistical probability distribution that represents the number of times an event occurs in a given time interval or space when the event is rare and independent of previous occurrences.

2. What are the characteristics of a Poisson distribution?

The characteristics of a Poisson distribution include discrete and non-negative outcomes, a single parameter (lambda) that represents the average rate of occurrence, and independence between occurrences.

3. How is the Poisson distribution different from other probability distributions?

The Poisson distribution differs from other distributions such as the normal or binomial distributions in that it is used to model rare events instead of continuous or binary outcomes. It also has only one parameter, unlike other distributions that may have multiple parameters.

4. What are some applications of the Poisson distribution?

The Poisson distribution is commonly used in fields such as biology, economics, and engineering to model rare events such as the number of mutations in DNA, the number of earthquakes in a certain area, or the number of defects in a product.

5. How is the Poisson distribution related to the law of rare events?

The Poisson distribution is related to the law of rare events, which states that as the number of trials or observations increases, the probability of a rare event occurring approaches a Poisson distribution. This is because rare events follow a Poisson distribution when they are independent and have a constant average rate of occurrence.

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